Measures of central tendency and of dispersion

Abstract

Most frequency and probability distributions of quantitative variates studied in biology may be interpreted using two opposite but complementary principles: the tendency of observations toward a central value on the one hand, and the dispersion of the same observations about that central value on the other hand. This state of things may be summarized algebraically by a model equation:

$$ X_{h = \mu + e_h ,} $$

where h is the subscript (order number) of the h ^th observation in a sample, X _h is the numerical value of that h^th observation,μis a constant value corresponding to the central tendency, and e _h is a random value which varies from each observation to the next one and accounts for dispersion. While the letter i is often used as a subscript, the letter h is preferred here because the letter i is saved for later use. Subtracting p from both members of the above model equation yields ${{e}_{h}} = \left( {{{X}_{h}} - \mu } \right)$ which shows that the random variable e _h corresponds geometrically to the distance (or deviation or deviate in statistical terminology) between the h^th observation X _h and the central tendency μ. Variation may be represented visually as a back-and-forth motion of an observed point X _h about an equilibrium point μ when an observation is succeeded by the next one(figure 4.1.1).